The ElGamal cryptographic algorithm is comparable to the Diffie-Hellman
system. Although the inventor, Taher Elgamal, did not apply for a
patent on his invention, the owners of the Diffie-Hellman patent (US patent 4,200,770) felt this
system was covered by their patent. For no apparent reason everyone calls this the "ElGamal" system
although Mr. Elgamal's last name does not have a capital letter 'G'.

A disadvantage of the ElGamal system is that the encrypted message
becomes very big, about twice the size of the original message m.
For this reason it is only used for small messages such as
secret keys.